The present invention relates generally to analysis of periodic signals and, more particularly, to a robust and accurate technique for measuring and characterizing waveforms of periodic signals, for example, in connection with testing and evaluating electronic circuits.
Measuring and characterizing periodic signals is an important part of a variety of technical fields including, for example, test instruments such as oscilloscopes and programmable test fixtures. In these technical fields, measuring and characterizing periodic signals typically includes determining the period, duty cycle and pulse width of the received signal. For example, oscilloscopes are commonly used to measure and characterize (display) the waveform of signals in electrical circuits. Based on certain measurements of sensed current or voltage in such signals, conventional oscilloscopes are adapted to characterize the waveform a function of detecting when the signal crosses a reference level. Using the reference level crossing, the waveform is typically characterized in terms of an estimated duty cycle and/or pulse width.
The accuracy of the waveform characterization is largely dependent on the algorithm used to provide this estimation. In one conventional algorithm, for example, the positive and negative pulse widths are determined by the difference in time between two consecutive crossings of the reference level with different polarities, and the period is determined by the difference in time between the third and first crossings with the same polarity. Another algorithm uses crossings of the reference level for real-time determination of period and frequency to analyze time-unlimited signals, such as human voice received via a microphone. For each of these approaches, the accuracy of the waveform characterization, or estimation, is dependent upon the processing of the parameters used to define the waveform, such as the pulse, duty cycle and pulse width of the waveform.
For applications involving the measurement and characterization of time-limited signals, including applications involving use of the digital oscilloscope, the received signal often includes undesirable spurious transitions. For conventional algorithms that characterize the received signal based on reference-level crossings, spurious transitions around the reference-level crossings can cause erroneous characterizations of the true signal. For example, the signal can be characterized to include a nonexistent polarity change.
Many such conventional algorithms use a xe2x80x9crelative reference level.xe2x80x9d The relative reference level is based on a reference level relative to the high and low voltage levels that determine the 100% and 0% levels, respectively. In many conventional test systems, the waveform middle reference level, MidRef, is typically user-set at 50% and is often used to define the positive duty cycle (D+) and amplitude levels. The waveform middle reference level is typically set at 50%. An ideal square waveform has infinitely sharp transitions and, hence, D+ has a well-defined meaning without regard to a reference level. In practical waveforms with finite transition slopes, D+ would depend on a reference level. Although the reference level does not commonly refer to an absolute level, in some applications, an absolute level has a meaning such as where an absolute DC level is used for a signal that goes into a charge pump, and the positive part of the signal pumps while the negative part pulls.
Assuming that the time at which the waveform s(t) crosses MidRef is denoted as tm, the slopes at the crossings should alternate in polarity and the period P can be defined as follows:
P=t3xe2x88x92t1xe2x80x83xe2x80x83(1)
If the waveform has a positive slope at the first crossing, the positive and negative pulse widths W+ and Wxe2x88x92 are calculated as follows:
W+=t2xe2x88x92t1 and Wxe2x88x92=t3xe2x88x92t2xe2x80x83xe2x80x83(2)
Otherwise,
W+=t3xe2x88x92t2 and Wxe2x88x92=t2xe2x88x92t1xe2x80x83xe2x80x83(3)
The positive and negative duty cycles D+ and Dxe2x88x92 are calculated as follows:
D+=W+/P and Dxe2x88x92=Wxe2x88x92/Pxe2x80x83xe2x80x83(4)
As mentioned above, using such a conventional crossings method to analyze and characterize a periodic waveform can be problematic. FIG. 1 depicts the measurement results of using this approach through illustrations of the period, positive and negative pulse widths and the positive duty cycle, with MidRef set at 50%. Because this waveform has significant undershoots that touch MidRef, the measured values of the period (P), the pulse width (W)xe2x88x92 and the positive duty cycle (D+) are erroneous. For further information pertaining to the above, and other related approaches, reference may be made to U.S. Pat. No.: 5,321,350, entitled, xe2x80x9cFundamental Frequency And Period Detector;xe2x80x9d U.S. Pat. No. 5,436,847 entitled, xe2x80x9cMethod For Determining A Periodic Pattern In A Line Spectrum;xe2x80x9d U.S. Pat. No. 5,592,390 entitled xe2x80x9cTime-based Method For Analyzing A Waveform;xe2x80x9d and U.S. Pat. No. 5,637,994 entitled, xe2x80x9cWaveform Measurement.xe2x80x9d
In view of the above, there is a need for improved approaches to the analysis and characterization of such period waveforms so as to mitigate their sensitivity to spurious transitions which can severely degrade the overall characterization of the sensed signal.
The present invention involves methods and arrangements directed to the accurate analysis of time-limited signal waveforms while avoiding significant delays and/or miscalculations due to the presence of spurious transitions. The present invention is exemplified in a number of implementations and applications, some of which are summarized below.
According to an example embodiment, the present invention is directed to a system and method for analyzing and characterizing a waveform of a time-limited signal having at least one period. For example, a processor may be configured and arranged to sense the signal and interpret various parameters of the waveform using a correlation method. In one application, the correlation method includes providing an autocorrelation function of a segment of the waveform that includes at least one of the periods, and approximating a period of the waveform using peaks in the autocorrelation function.
In more specific applications, the above correlation method also includes approximating the period of the waveform by identifying a segment of the waveform having a slope that exceeds a certain threshold, and determining a polarity associated with the period of the waveform.
Other example embodiments are directed to providing data corresponding to a comparison waveform segment, measuring a time difference between consecutive maximum and minimum levels of a segment of the time-limited signal, and determining the polarity of the segment by cross-correlating the data corresponding to the comparison waveform segment and data corresponding to the segment of the time-limited signal.
In yet other embodiments of the present invention, the autocorrelation function represents a measure of correspondence between the segment of the waveform and a time-shifted version of the segment of the waveform. For example, in more specific embodiments, the autocorrelation function represents a measure of similarity of the segment of the waveform with a time-shifted version of the segment of the waveform, and the measure of similarity is greatest where the segment of the waveform, relative to the time-shifted version, is shifted one complete period. In an alternative embodiment, the autocorrelation function represents a measure of dissimilarity of the segment of the waveform with a time-shifted version of the segment of the waveform, and the measure of dissimilarity is greatest where the segment of the waveform is shifted relative to the time-shifted version by an amount corresponding to a pulse width of the waveform.
The above summary of the present invention is not intended to describe each illustrated embodiment or every implementation of the present invention. For example, in other embodiments, various aspects of these embodiments are combined. The figures and detailed description which follow more particularly exemplify these embodiments.